Why would an Italian astronomer want an infinite set? What paradox did Galileo exploit?

What did Galileo do with Infinite Sets and Paradoxes?

Galileo Galilei, the famous Italian astronomer, wrote a book in which he tried to prove that a long line segment and a short line segment had the same “number” of points, even though one was obviously longer than the other.

How did Galileo demonstrate his paradox? Is it a convincing argument, or did he slip up with his infinite sets?

My article, “The Paradox of the Infinite Series of Squares Numbers by Galileo” in Decoded Science, explains how Galileo presented this charming paradox.

As always, I also publicized this article in my Blog of Writing, where “Preview of Galileo and his Paradox of Squares” includes the preview of images I made for the article as well as my “writing tip”
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Thank you for reading about Galileo’s paradox of infinite sets.